Question

Analyze the end behavior of both functions.

a. f(x) = x, g(x) = 1 / x
b. f(x) = x3, g(x) = 1 / x3
c. f(x) = x2, g(x) = 1 / x2
d. f(x) = x4, g(x) = 1 / x4
e. f(x) = x − 1, g(x) = 1 / x − 1
f. f(x) = x + 2, g(x) = 1 / x + 2
g. f(x) = x2 − 4, g(x) = 1 / x2 − 4

Answer 1

The end behaviour of all the functions is same ie they all tend to zero.

Explanation:

In every option the function f(x)is a linear function which tends to infinity at the end(as x tends to infinity).Now the function g(x)in every option is just the reciprocal of f(x).As we all know

`\lim_(n \to \infty) f(x)=`∞

then

`\lim_(n \to \infty) 1/f(x)=0`